Name: Period: Date: 2. How is the ball s acceleration related to the force Julia applies to the ball?

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1 Name: Period: Date: IMPULSE AND MOMENTUM CONTENTS Impulse and Momentum... 1 Background... 1 The Concepts of Impulse and Momentum... 2 Relationship to Newton s Second Law... 4 Journaling Assignment... 5 Calculating Momentum and Impulse... 5 BACKGROUND 1. Julia is pushing a field hockey ball down the hallway with the stick so that she is applying a constant force to the ball. Assuming that friction does not change much with velocity, what happens to the ball? 2. How is the ball s acceleration related to the force Julia applies to the ball? 3. If the ball was at rest when Julia started applying the force, what equation would you use to describe the final velocity of the ball? 4. How is the final velocity of the ball related to the length of time that Julia applies the force? 5. How is the final velocity of the ball related to the magnitude of the force Julia applied? 6. If Julia replaces the ball with one that had twice the mass, what two things could she do to get the ball up to the same speed as the less massive ball? 1

2 THE CONCEPTS OF IMPULSE AND MOMENTUM In everyday physics you can observe that how quickly you can change the motion of an object depends on strength of the net force acting on the object, the length of time the force acts, and the mass of the object. Physics use two new terms to describe these changes: Both impulse and momentum are vector quantities. Impulse is always in the same direction as the net force on an object, while momentum is in the same direction as an object s velocity. Just like our velocity and displacement vectors in projectile motion, we could divide impulse and momentum vectors into components in the horizontal and vertical directions. It is important to understand that the time in the impulse equation refers to the interaction time or the time that the net force is applied. This will be important when we think about changes in momentum during collisions. Your everyday experiences tell you that the more momentum an object has, the more force you need to exert over a given amount of time to stop it. Alternatively, you could exert less force over a longer time to bring the object to a gentler stop. What you are observing is that there is a relationship between impulse and the change in momentum of an object. This relationship is can be expressed as an equation The larger the impulse you apply to an object, the more you will change the object s momentum and velocity. The larger the mass of the object, the larger the impulse you need to exert on it to get the same change in its velocity. You can apply a larger impulse by either pushing harder or pushing for a larger amount of time. 7. Which has more momentum, a loaded dump truck going at 70 mph due west or a sports car going at 70 mph due west? 8. What is the direction of the sports car s momentum? 9. If both drivers saw a crash ahead so they needed to stop in 2 s, which would require a larger force to stop in that amount of time? 10. Which would require a larger impulse to be exerted to stop in time? 2

3 11. Air bags are used in cars as a safety feature to protect front-seat passengers. This safety feature helps to protect the passengers of the car by increasing the and decreasing the. 3

4 RELATIONSHIP TO NEWTON S SECOND LAW The impulse/change in momentum relationship is really just another way to look at Newton s Second Law that said First let s multiply each side of the equation by mass and time and use the definition of impulse to get But we also know from our study of motion that the definition of acceleration is the change in velocity divided by the time or If we substitute in the definition of acceleration into the previous equation we can see that 4

5 JOURNALING ASSIGNMENT In your blog: Define impulse and momentum Give some examples of large impulse vs. small impulse and large momentum vs. small momentum Describe in your own words how impulse and momentum are related A car traveling to the right experiencing a net force to the left. What could be happening to cause this situation? CALCULATING MOMENTUM AND IMPULSE There are no special units for impulse and momentum. We can see that impulse needs to be in N s and momentum is in kg m/s. These two groups of units are in fact equal to each other since we know that 1 N is the force required to accelerate 1 kg at a rate of 1 m/s If I triple the net force on an object what will happen to the impulse? To the change in momentum? 13. If I exert the same net force on an object for twice as long, what will happen to the impulse? To the change in momentum? 14. If I exert the same impulse on an object that is five times more massive, what will happen to the change in the object s momentum? To the change in the object s velocity? 15. Is the relationship between net force and impulse direct or inverse? 16. Is the relationship between net force and change in momentum direct or inverse? 17. A rightward moving object is slowing down. The direction of its momentum is. The direction of its acceleration is. 5

6 18. A ball moves in the direction of the arrow labeled e below. The ball is struck by a stick which briefly exerts a force on the ball in the direction of the arrow labeled g below. Which arrow best describes the direction of, the change in the ball's momentum? 19. What is the momentum of a 15 kg dog chasing a rabbit north at 4 m/s? What do you know? Which equation will you use? What is the solution? 20. A good sprinter can run 100 meters in 10 seconds (a speed of 10 m/s). What is the magnitude of the momentum of a sprinter whose mass is 60 kg and who is running at a speed of 10 m/s? 21. The momentum of a 1350-kg car is equal to kg m/s North. What is the velocity of the car? 22. A 60-kg object is moving at 20 m/s when a force brings the object to rest in seconds. If the same object moving at the same initial speed was brought to rest in 0.50 seconds, then the required force would be, the resulting impulse would be and resulting momentum change would be. 23. An object with a mass of 20 kg moves with a constant velocity of 3.0 m/s for a time of 6.1 seconds. What is the momentum of the object? 6

7 24. An object with a mass of 30 kg is initially at rest. The object now moves with a constant velocity of 6.0 m/s. What impulse was imparted to the object? 25. An object with a mass of 65 kg is initially at rest. The object now moves with a constant velocity of 8.0 m/s. What is the change in momentum of the object? 26. An object with a mass of 52 kg s is initially at rest. A force of 80 N is applied to the object for 6.1 seconds. What is the final momentum of the object? 27. An object with a mass of 85 kg s is moving with a velocity of 6m/s. The object encounters a resistive force of 26 N for 3.3 seconds. What is the new momentum of the object? 28. A baseball has a mass of about 155 g. What is the magnitude of the momentum of a baseball thrown at a speed of 93 miles per hour? (Note that you need to convert mass to kilograms and speed to meters/second. A mile is 1.6 kilometers or 1600 meters.) 7